I. INTRODUCTION. Electronic mail: b J. A. Colosi, B. D. Cornuelle, B. D. Dushaw, M. A. Dzieciuch, B. M.

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1 Extracting coherent wave fronts from acoustic ambient noise in the ocean Philippe Roux, a) W. A. Kuperman, and the NPAL Group b) Marine Physical Laboratory of the Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California Received 16 May 2003; revised 24 June 2004; accepted 16 July 2004 A method to obtain coherent acoustic wave fronts by measuring the space time correlation function of ocean noise between two hydrophones is experimentally demonstrated. Though the sources of ocean noise are uncorrelated, the time-averaged noise correlation function exhibits deterministic waveguide arrival structure embedded in the time-domain Green s function. A theoretical approach is derived for both volume and surface noise sources. Shipping noise is also investigated and simulated results are presented in deep or shallow water configurations. The data of opportunity used to demonstrate the extraction of wave fronts from ocean noise were taken from the synchronized vertical receive arrays used in the frame of the North Pacific Laboratory NPAL during time intervals when no source was transmitting Acoustical Society of America. DOI: / PACS numbers: Pc, Rq, Fg WLS Pages: I. INTRODUCTION Acousticians have used incoherent processing of ambient noise to achieve small scale imaging in the ocean 1 in the same way as optical imaging is performed from incoherent light. Here, we show that it is feasible to transform a collection of apparently incoherent noise sources into a coherent, large scale, imaging field. Actually, every individual source of noise e.g., a collapsing bubble in the ocean generates an acoustic field that is potentially coherent when received between two points after long range propagation. However, this small coherent component at each receiver point is buried in the spatially and temporally incoherent field produced by all the widespread noise sources distributed over the ocean. We demonstrate in this paper that a long-time cross-correlation process extracts coherent wave fronts from ambient noise without the support of any identifiable source. This means that noise could be used as a potential coherent source in the ocean leading to the concept of a self-imaging process. These general results reveal the potential information content of random noise fields in a natural environment. The sources of ocean surface noise 2 4 natural and manmade as well as the subsequent average spatial distribution of ocean noise 5 7 have been studied extensively. However, because the instantaneous distribution of all the mutually incoherent sources is extremely variable in space and time, a robust, space time observable of ocean noise is difficult to identify. In this work, we derive and verify with data a space time wave-front coherence property of surface noise not previously explored. With simple signal processing these wave fronts that are strongly related to the time-domain Green s function TDGF between observation points, are easily observable. Though incoherent imaging with ambient noise has been demonstrated, 1,8 the goal of this research is to lay the foundation for substituting ambient noise in coherent imaging procedures such as tomography 9 that typically require an active source or other noise based imaging methods in need of some coherence e.g., Ref. 10. The results presented here find their origin in the helioseismologic research of Rickett and Claerbout. 11 Their work is based on the following conjecture: By cross-correlating noise traces recorded at two locations..., we can construct the wavefield that would be recorded at one location if there was a source at the other. This statement has been experimentally confirmed by the ultrasonic research of Weaver and Lobkis, 12,13 who have shown that the long-time, two-point correlation of random Brownian motion noise in an aluminum block cavity yields the deterministic time-domain Green s function between the two points. Further, there have been recent results of a related nature by Campillo and Paul 14 based on the cross correlation of the diffuse coda of identifiable seismic events. Here, we demonstrate that the temporal arrival structure of the two-point acoustic TDGF can be analogously approximated in the ocean using ambient noise. In particular, the long-time correlation between a receiver and elements of a vertical array of receivers yields a wavefront arrival structure at the array that is identical to the structure of the TDGF except that the amplitudes of the individual wave fronts are shaded by the directionality of the noise sources. The Green s function emerges in both the cavity and ocean cases from those correlations that contain noise sources whose acoustic field passes through both receivers. The Weaver result relies on noise sources that are contributing to the construction of the TDGF that are distributed over three dimensions 3D leading to the so-called modal equipartition in the cavity. The Campillo result is also based on modal equipartition, 15 in this case due to multiple scattering in the earth upper crust, but they build up their TDGF from a set of identifiable events. For the ocean environment considered here, there is no significant 3D scattering in the frea Electronic mail: philippe@mpl.ucsd.edu b J. A. Colosi, B. D. Cornuelle, B. D. Dushaw, M. A. Dzieciuch, B. M. Howe, J. A. Mercer, W. Munk, R. C. Spindel, and P. F. Worcester. J. Acoust. Soc. Am. 116 (4), Pt. 1, October /2004/116(4)/1995/9/$ Acoustical Society of America 1995

2 FIG. 1. a Two arrays are depicted at a separation distance R. A schematic of the directivity pattern of the time-domain correlation process between two receivers on each array is projected on the ocean surface. Only a discrete set of lobes have been displayed that correspond to noise sources whose emission angle is equal to 60, 30, 0, 30, 60, and 90. Each angular lobe depends on the central frequency and bandwidth and corresponds to a delay time in the correlation function. For the case of equally distributed ambient noise sources, the broad end-fire directions will contribute coherently over time to the arrival times associated with the TDGF while the contribution of the narrow off-axis sidelobes will average down. For the case of shipping noise, coherent wave fronts emerge only when there is sufficient intersection of the shipping paths with the end-fire beams. However, if there is a particular loud shipping event, it will dominate so that either impractically long correlation times are needed, or discrete events should be filtered out. b and c The correlation process is done using time-domain ambient noise simultaneously recorded on two receivers in arrays 1 and 2. d Spatial temporal representation of the wave fronts obtained from the correlation process between a receiver in array 1 at depth 500 m and all receivers in array 2 separated by a distance R2200 m. The arrival structure of the correlation function is composed of the direct path, surface reflected, bottom reflected, etc., as expected in the TDGF. Because data were taken in 20 min segments, the result is a combination of three segments in order to accumulate the wave-front structure from what turns out to be shipping noise see Fig. 7 for further explanation. The correlation function is plotted in a db scale and normalized by its maximum. e The same correlation processing is performed on data that have not been recorded at the same time on the two arrays. In d and e, the x and y axes correspond to the time axis of the cross-correlation function and receiver depth, respectively. The correlation functions are plotted in a db scale and normalized by the maximum of d. quency regime of the available data. Without the presence of identifiable events, it is shown that only noise sources aligned along the line between the receivers contribute over a long-time correlation. This paper is structured as follows. In Sec. II, we describe the basic principles of the ambient noise crosscorrelation technique in the ocean. Section III presents experimental results using a known shipping source verifying that the residual of the time-averaged correlation function indeed comes from noise sources located in the endfire direction of the receivers. Section IV starts with a theoretical derivation of the ambient noise time-domain correlation function with noise sources distributed either in the volume or at the surface of the waveguide. The case of shipping noise is also explored. Simulations in shallow water point out the similarities and differences with the TDGF. Finally, we present in Sec. V coherent wave fronts obtained from ambient noise data simultaneously recorded on four coplanar hydrophone arrays. II. BASIC PRINCIPLES AND EXPERIMENTAL DEMONSTRATION The overall concept is summarized in Fig. 1 in which ambient noise at two receivers Figs. 1b and 1c in array 1 and array 2 are pairwise cross-correlated. In Figs. 1d and 1e, this correlation is a function of delay time and vertical position depths of receivers in array 2 as is the TDGF between a position in array 1 and the receivers of the array 2. The directivity pattern of the correlation process for a set of incoming angles is schematically projected on the ocean surface Fig. 1a. For each incident angle, the directivity beam depends on the central frequency and bandwidth see Sec. III for details and corresponds to a delay time in the correlation function. This directivity pattern shows how noise sources all over the ocean surface participate to the noise crosscorrelation function. Noise sources inside the same directivity beam add coherently while noise sources inside different directivity beams average incoherently i.e., there is a different delay time associated with each beam. In Fig. 1a, we see that two broader beams so called end-fire beams are 1996 J. Acoust. Soc. Am., Vol. 116, No. 4, Pt. 1, October 2004 Roux et al.: Coherent wave fronts from ambient noise

3 aligned on the axis between the two arrays. Because of their size, these beams yield a larger contribution to the noise correlation function. For example, the two dashed lines in Fig. 1a show the coherent contribution from surface noise sources that travel through both receivers. We will show in Sec. III that noise sources inside the end-fire beams provide the residual time-averaged coherence between the two arrays. In Fig. 1d we show a display that is an actual multiday composite of three 20 min segments of simultaneous recordings of data discussed in Sec. IV. The wave fronts in the display obtained from the cross-correlation process are symmetric in time with respect to the zero time of the correlation function because noise sources were distributed on both sides of the arrays. Note that there is no correlation between data not recorded at the same time Fig. 1e confirming the hypothesis that coherent wave fronts built up over time from individual noise sources whose acoustic field propagates through both receivers. The basic difference between the Weaver cavity configuration and ocean noise is the 3D reverberation physics of the cavity versus the two-dimensional ocean waveguide physics of traveling waves in the horizontal direction. For the latter, this means that a ray aligned along the receiver axis will pass through both receiver points by reflection or refraction; however, if the ray has a horizontal component not along the horizontal line between the receivers, it cannot be reflected back to the second receiver and therefore cannot contribute to building up the coherent wave fronts between the receivers. This geometrical interpretation does not apply to the cavity but is still valid in the case of Campillo s multiple scattering earth model. Indeed, even if the seismic events are not aligned with the two seismometers, we believe that the main contribution to the average correlation function comes from the scatterers present inside the end-fire beams. Indeed, the direct path is built from those scatterers in the upper crust of the earth that behave as secondary sources and re-direct the incident field so that part of the wave travels on a straight line through both receivers. III. EXPERIMENTAL DEMONSTRATION OF LONG- TIME TWO-POINT CORRELATION PROCESSOR The underlying physics of this technique relies on longtime cross correlation of ambient noise data. Cross correlation of acoustic data between hydrophones is a very common signal processing tool to detect and locate sources in the ocean. The difference here is that we are not interested in the actual noise sources but in the residual coherence between the hydrophones. This coherence, which corresponds to the temporal arrival structure of the TDGF, is extracted when the cross correlation is performed on long-duration time series. In the case of nonstationary noise sources surface noise or noise generated by a ship in motion, the signature of the noise sources in the cross-correlated signal averages out and disappears while the coherent paths between the two hydrophones remain. A separate experimental demonstration of this process has been performed from data simultaneously recorded on two sono-buoys at a few hundred meters from each other in FIG. 2. Representation in latitude-longitude coordinates of the 16-min-long ship track blue full line with respect to the sono-buoys location blue *. The approximate distance between the sono-buoys is R650 m. The average ship speed was constant and equal to 4.8 m/s. The directivity pattern of the time domain cross-correlation process between the two sono-buoys is plotted in red. Only a discrete set of lobes have been displayed that correspond to noise sources whose emission angle is equal to 60, 30, 0, 30, 60, and 90. a shallow water environment. Noise was generated during 16 min in the Hz frequency interval by a ship whose track is represented in Fig. 2. The two 16-min-long time series are then cross correlated using different time windows Fig. 3. When the correlation is performed on 1 s duration time series Fig. 3a, the ship track is clearly observed. If the length of the cross-correlated time series is increased to 5, 10, 20, and up to 30 s Figs. 3b 3e, respectively, the signature of the ship track tends to disappear and the only signal left is obtained when the ship crosses the end-fire main lobes Fig. 2. This signal exhibits different bottom and surface-reflected paths classically found in a shallow water environment. We will show in Sec. IV that it converges to the arrival structure of the TDGF between the two sonobuoys when averaged over several different ship tracks. Obviously, we observe in Figs. 3a 3e that the longer the correlation window, the higher the signal-to-noise ratio because more acoustic sources participate coherently to correlation function. Then, for longer time series Fig. 3f, the correlation pattern does not change because no more coherent sources were present in the signal. Assuming that the speed of the ship was constant during the track, it generates a uniform density of sources over time. For long time windows, the signal-to-noise ratio of the correlation process can be defined as the ratio of the number of coherent versus incoherent sources inside the recording time window. Following the geometrical interpretation developed in Sec. II, this ratio corresponds to the area enclosed by the end-fire beam to a non-end-fire beam. The directivity pattern B(, 0 ) in the direction of the correlation function between two receivers for an incident wave in the direction 0 can be written as B, 0 /2 /2 1exp i R c cos 1exp i R c cos 0d, 1 where R is the distance between the two receivers, 2 f J. Acoust. Soc. Am., Vol. 116, No. 4, Pt. 1, October 2004 Roux et al.: Coherent wave fronts from ambient noise 1997

4 FIG. 3. Representation of the temporal evolution of the time-domain cross-correlation function between the two sono-buoys along the 16-min-long ship track. The x and y axes correspond to the time axis of the correlation function and the ship position, respectively. The duration of the time windows on which the cross correlation is performed is a 1s,b 5s,c 10 s, d 20 s, e 30 s, and f 40 s. Each cross-correlation pattern is normalized by its maximum. The color scales are in db. the central angular frequency, and the frequency bandwidth. The angle and 0 are defined with respect to the axis of the two receivers. After development and integration, we obtain the following from Eq If 0 0 and 0, B 0, R sin 0 c 2 If 0 0or 0 and 0, B,0B,1 4 8 R c Equations 2 and 3 show that the end-fire beams for 0 0or 0 ) are broader. It follows that the ratio of the area enclosed by the end-fire beam to a non-end-fire beam is Ratio 0 c R sin /4. 4 Taking R650 m, f f 200 Hz, c1500 m/s we get a maximum signal-to-noise ratio of 25 db, which is in good agreement with the data Fig. 3e. The maximum signal-tonoise ratio is obtained for a time window T30 s that is approximately the time spent by the ship in the end-fire beam. IV. THEORY AND SIMULATION The analogy to the Weaver volume cavity noise would ideally be ocean volume noise sources uniformly distributed throughout the water column. However, ocean noise is dominated by surface noise sources that are typically uniformly distributed over the ocean surface as one goes to higher frequencies 1 khz, see Ref. 2. For the lower frequency case 100 Hz, data are dominated by shipping noise, and while the concept remains the same, the relative amplitudes of the wave fronts that become observable will be dependent on the specific shipping distribution during the recording time interval. As a matter of fact, it is shown here by theory and FIG. 4. Schematic of the waveguide in which simulations are performed. A source receiver in z m and an array of receivers are located at a distance R2500 m from each other in a 150-m-deep shallow water environment. The surface noise sources are at depth z1 m. The sound-speed profile decreases linearly from 1500 m/s at the surface to 1480 m/s at the bottom. The bottom sound speed, density, and attenuation are 1800 m/s, 1800 kg/m 3, and 0.05 db/, respectively J. Acoust. Soc. Am., Vol. 116, No. 4, Pt. 1, October 2004 Roux et al.: Coherent wave fronts from ambient noise

5 simulation that shipping produces similar results to the surface noise case but that distant shipping emphasizes more horizontally traveling wave fronts than nearby ships for which the wave fronts are more vertical. The ocean acoustic environment is typically treated as a waveguide 16 such that the propagation between points 1 at depth z 1 and 2 at depth z 2 separated by horizontal range R Fig. 4 is given, in its simplest form, by a normal mode expansion: G R,z 1,z 2 is U 4 n z 1 U n z 2 H 1 0 k n R, 5 n where U n (z) is the depth-dependent eigenfunction associated with wave number k n, is the density at the source location, and S() is the source spectrum. When integrated over the frequency bandwidth, Eq. 5 becomes the TDGF: G t R,z 1,z 2 d G R,z 1,z 2 expit. The wave-front structure of the Green s function results from modes with similar group speeds constructively interfering over frequency; mathematically the wave fronts can be shown to emerge, for example, from a stationary phase evaluation 17 of Eq. 6 that results from the condition d(k n Rt)0. A. Volume-noise case In order to demonstrate the connectivity between the volume-cavity result of Weaver and the correlation of ocean waveguide noise as formulated by Kuperman and Ingenito, 6,16 we first modify the latter theory to include volume sources. This shows how the waveguide TDGF emerges in analogy to the cavity case. Following Ref. 6, the modal decomposition in the frequency domain of the volume noise cross-correlation function between points 1 and 2 is C R,z 1,z 2 iq2 k z dz n,m U n zu n z 1 1 U m zu m z 2 k 2 n k m * 2 H 0 1 k n RH 0 1 k m *R, where Q 2 () is the power spectrum of the noise sources and z the depth of the noise sources. To obtain Eq. 7, we assumed that each sheet of noise sources at depth z are uncorrelated and that noise sources are uniformly distributed in the whole water column. The spatial integration over the depth of the waveguide can be performed using the orthogonality condition of modes U nzu m z dz z nm. Doing so, we neglect the tail of the mode in the bottom of the waveguide and we assume a constant density in the water column (z). We also suppose that k n is a complex number of the form k n K n i n with K n n 0), where n is the modal attenuation coefficient. The final expression 6 7 for the ambient noise correlation function is then: C R,z 1,z 2 Q2 4k 2 n 1 U n z 1 U n z 2 n K n H 0 1 k n RH 0 1 k n *R. After frequency integration, the time-domain ambient noise correlation function is obtained from C t (R,z 1,z 2 ) d C (R,z 1,z 2 )exp(it). The two Hankel functions in Eq. 8 represent two wave fronts traveling between receivers 1 and 2 in opposite directions. Physically speaking, the two wave fronts arise from a uniform volume noise distribution so that at any point, noise is coming from all directions. Invoking the modal normalization condition, U n 2 (z)/ (z)dz1, the amplitude factor n K n z cz U n 2 z z dz where z is the depth-dependent absorption 16 is slowly dependent on mode number. Thus, the modal decomposition in Eq. 8 is very close to the Green s function decomposition as written in Eq. 5. This means that the correlation function obtained from volume ambient noise recorded at two receivers in a waveguide is a good approximation of the Green s function between the two points. The reasoning done through Eqs. 7 and 8 is the waveguide equivalent of Weaver s cavity approach in which he supposed the modes equipartition due to an uniform noise distribution in the cavity. B. Surface-noise case Assuming a sheet of noise sources located at a given depth z only, Kuperman and Ingenito obtained the following expression for the noise correlation function: Q2 C R,z 1,z zk 2 n U n z 1 U n z 2 U n 2 z H 1 n K 0 k n RH 1 0 k n *R. n 9 In the case of noise sources distributed at the surface of the ocean, a monopole source below the pressure release ocean surface behaves as a dipole structure. The amplitude factor U 2 n (z)/ n K n in Eq. 9 results then from a combination of the dipole behavior of the noise sources and the effect of attenuation over long ranges. Formally, the factor arises because there is no integral over the depth of sources as in the volume case; that is the only difference between the volume and surface cases. Since this amplitude term will not affect the stationary phase argument that synthesizes the wave fronts, 18 the time-domain surface noise correlation function C t (R,z 1,z 2 ) will exhibit the same wave-front structure as the two point Green s functions though the amplitude of the wave fronts will be different. We therefore conclude that 8 J. Acoust. Soc. Am., Vol. 116, No. 4, Pt. 1, October 2004 Roux et al.: Coherent wave fronts from ambient noise 1999

6 FIG. 5. Spatial-temporal representation in a linear scale of a the timedomain cross-correlation function of surface noise computed between a receiver in z m and a receiver array at a distance R in a shallow water waveguide see Fig. 4. The x and y axes correspond to the time axis of the correlation function and the receiver depth, respectively. b The time domain Green s function TDGF computed between a source in z 1 and a receiver array at the same distance R; c the TDGF computed in the same configuration as in b for a vertical dipole source at z 1. Simulations have been performed in the Hz frequency bandwidth. after the temporal averaging underlying Eq. 9, we obtain coherent wave fronts from ocean surface noise. However, these coherent wave fronts only constitute an approximation of the TDGF, the excitation of each mode being weighted by a dipole shading. This approach is similar to Campillo s result in the sense that only the Rayleigh wave was reconstructed between two seismometers using the late coda of seismic events. The longitudinal and shear waves that classically participate to the TDGF between two points at the earth surface are missing in the correlation function because they are not properly excited by the scatterers present in the upper crust of the earth. In Fig. 5, we confirm this theoretical approach with simulations using the spectral model 19 performed in a shallow water environment in the Hz frequency bandwidth Fig. 4. The time-domain correlation function of surface noise Fig. 5a is compared to the actual Green s function Fig. 5b between one source-receiver and an array of receivers. As expected, the same coherent wave fronts are observed but the amplitude of the higher-order reflected paths is different. Consistent with the above-mentioned results, the Green s function computed with a vertical dipole source instead of an omnidirectional monopole excitation Fig. 5c shows an obvious similarity with the time-domain correlation function. C. Shipping-noise case For the pure shipping case, the correlation function results from the product of two Green s functions each of the form given in Eq. 5 but evaluated at the radial distances R 1 and R 2 between the ship and receivers 1 and 2, respectively: Q 2 C R,z 1,z 2 U 2 n zu n z 1 U m z z n,m U m z 2 H 1 0 k n R 1 H 1 0 k m R 2, 10 where Q 2 () is the power spectrum of the shipping noise. As explained in Sec. III, the correlation process emphasizes the contribution from ships located in the end-fire beams. When a ship is located in the end-fire direction of the two receivers, we have R 1 R 2 R. Evaluating the average contribution from a ship involves integrating Eq. 10 over the length L of the ship track inside the end-fire beam see Fig. 1a yielding an amplitude term sin c((k n k m )(L/2)), where sin c(x)sin(x)/x stands for the sinus cardinal function. When the integration is performed on several ship paths whose accumulated path L is such that 1 L min n,m k n k m, it follows: C R,z 1,z 2 Q 2 2 z n U 2 n z U n z 1 k n U m z 2 H 0 1 k n R, 11 where the angular brackets refer to the average over an accumulation of ship events. When ship paths cover the whole ocean surface, the propagating wave in Eq. 11 is changed into two propagating waves in opposite directions as in Eq. 9. Equations 11 and 9 then become very similar in the sense that they both correspond to an amplitudeshaded approximate version of the TDGF. Though we get the same forms for either broadband shipping or surface ambient noise, the signal-to-noise ratio emergence of the wave fronts of the two cases will be different as the schematic of Fig. 1 indicates and as discussed further in the following. For example, as opposed to ambient noise sources, shipping events could be possibly identified, normalized in amplitude, and integrated separately in the correlation function. This would balance the contribution of close/faraway ships with loud/low source levels. Furthermore, since shipping is episodic, it would be helpful to elimi J. Acoust. Soc. Am., Vol. 116, No. 4, Pt. 1, October 2004 Roux et al.: Coherent wave fronts from ambient noise

7 FIG. 6. Simulations of the Green s function TDGF and the time domain correlation function in an oceanic environment close to the experimental data. a Spatial-temporal TDGF from a source at depth 800 m to an array at a distance of 2400 m. b The same TDGF but source shaded by a dipole pattern similar to the radiation pattern of near-surface sources. c Surface noise correlation function between the same position of the source and the array showing a close similarity to b. The x and y axes correspond to the time axis of the correlation function and the receiver depth, respectively. The color scales are in db. nate high amplitude events from the data and thereby homogenize the noise in order to enhance the convergence to the expected correlation function. The best data set displays no specific events and is approximated well by the theory of uniformly distributed surface noise sources. Simulations of the above-noted processes are given in Figs. 6 and 7 in which the TDGF is numerically computed with the surface noise correlation function or the shipping events correlation function. The ocean environment is close to the experimental configuration described in Sec. V Fig. 8a. As in Fig. 5, when the Green s function Fig. 6a is combined with the directivity of a dipole Fig. 6b, the depth-time dependent pattern of the Green s function and the noise correlation function Fig. 6c look similar. However, the amplitudes of the wave fronts are still different because a dipole at 600 m does not have the same directivity pattern as a dipole at the surface in a depth-dependent sound speed profile. Further, Fig. 7 refers to an end-fire ship track source contributions from other directions vanish over long correlation time window, as shown in Fig. 3 at different ranges. In Figs. 7a 7c, we observe that the wave-front arrivals have FIG. 7. Spatial temporal representation of the correlation function obtained in the case of near-surface sources shipping noise at various ranges in an oceanic environment close to the experimental data. The x and y axes correspond to the time axis of the correlation function and the receiver depth, respectively. a An L500 m track for a ship at a 20 km distance. b An L500 m track for a ship at a 3.5 km distance. c An L500 m track for a ship at a 500 m distance. d Composite of a, b, and c indicating what one could expect from an accumulation of shipping episodes. The color scales are in db. different amplitude emphasis shorter ranges favoring more vertical paths in the correlation function. Figure 7d, which is a composite of the various ranges, exhibits, as expected, the same arrival structure as in Fig. 6a. Hence, in the shipping case, a collection of random shipping events will fill in the whole TDGF pattern over time. Roux and Fink 20 have theoretically examined the case of averaging correlations of deterministic sources over depth that theoretically results in modal equipartition. 12,14 However, as an impractical matter in ocean acoustics, it requires the insertion of active sources and is more akin to the above-discussed hypothetical volume source problem. J. Acoust. Soc. Am., Vol. 116, No. 4, Pt. 1, October 2004 Roux et al.: Coherent wave fronts from ambient noise 2001

8 FIG. 8. The noise-derived amplitude-shaded TDGF extracted from the NPAL data. a The array geometry indicating a sloping bottom. Note that array 4 is made of twice as many elements as arrays 1 3. b d Time-domain correlation functions between a receiver at depth 500 m in array 1 and all receivers in the other arrays. Traveling wave fronts are clearly observed in the direction of the arrow as if they emanated from the receiver in array 1. e, f, and g Time-domain correlation functions between a receiver at depth 500 m in array 4 and all receivers in the other arrays. Here we see traveling wave fronts in the direction of the arrow, opposite case b, c and d, as if they emanated from the receiver in array 4. The wave fronts for this direction are more vertical because of the slope effect further confirming the correct extraction of the arrival structure of the TDGF. In b g, the x and y axes correspond to the time axis of the correlation function and the receiver depth, respectively. The color scales are in db. V. EXPERIMENTAL RESULTS WITH HYDROPHONE ARRAYS The actual measurement and signal processing that correspond to the theoretical results of Eq. 9 is done in the time domain where the correlation function C 12 (t) is measured using C 12 (t) S 1 ()S 2 (t)d, where S 1 (t) and S 2 (t) are the ambient noise received on receivers 1 and 2 at time t. Note that the correlation processing requires data measurement that have a common clock time. We use data of opportunity from the NPAL program 21 originally taken for other purposes. Data correspond to different sets of 20 min simultaneous recording of ambient noise on four vertical arrays, filtered between 70 and 130 Hz. Despite the obvious presence of shipping noise in this frequency bandwidth, high amplitude signals were not identifiable in the spectrograms at the receivers. Using four coplanar arrays Fig. 8a enables us to measure the noise correlation function with respect to the travel time separation between one receiver in array 1 and all receivers in arrays 2 4 as shown in Figs. 8b 8d. Note in Figs. 8a and 8d that array 4 has twice as many elements as arrays 1 3. We observe from the correlation lag times that we have extracted wave fronts as they would propagate from a point source to ranges of 1700, 2400, and 3500 m, respectively. We also show that we recover similar wave fronts for the opposite direction by correlating one receiver in array 4 with all receivers in arrays 1 3 Figs. 8e 8g. The sloping environment results in the asymmetry between the two directions, i.e., upslope increases the reflection angle. From the physical picture and the measurements presented above we can derive insight into the major components governing the rate of emergence of the coherent wave fronts for a homogeneous distribution of random sources. However, we can only draw some qualitative insight into our specific data of opportunity that is dominated by episodic shipping. Consider two receivers separated by a distance R. The signal-to-noise ratio SNR at the output of the correlation depends on three physical phenomena. First, it depends on the part of the signal that contributes to the correlation compared to the uncorrelated ambient noise, either acoustic or electronic. The uncorrelated acoustic ambient noise corresponds to the field that does not reach the two receivers because of the medium attenuation or above critical grazing angle transmission into the bottom. That is, the noise field consists of a local and some nonlocal components which vary with overall attenuation. Second, the correlation function is built from the contribution of noise sources located in the end-fire beams versus noise sources in the non-end-fire beams cf. Eq. 4. Last, for a bandwidth f, the SNR associated with a correlation process grows with recording time T and is given by T f. 18,22 In any event, the total SNR at the end of the correlation process is related to the 2002 J. Acoust. Soc. Am., Vol. 116, No. 4, Pt. 1, October 2004 Roux et al.: Coherent wave fronts from ambient noise

9 time bandwidth product, the spatial structure of the correlator as described in Eq. 4, and an environmental factor expressions for local versus long range contributions given in Refs. 23 and 24, the latter typically being not known for an arbitrary location. Without specific environmental knowledge, the rate of emergence TDGF is a measured parameter that can be used to estimate the bottom geophysics since volume attenuation is typically known. These arguments are for homogeneous ambient noise; the additional complication of shipping noise requires a long enough measurement period that demonstrates convergence. VI. CONCLUSION Our results demonstrate the potential information content of a random noise field. In particular, we have demonstrated through theory and data analysis that we can recover coherent deterministic wave fronts related to the structure of the time domain Green s function using measurements of ocean ambient noise between vertical arrays. In the NPAL data analysis, we have used the 20 min data blocks that were available and it is not likely that we have done sufficient time averaging for the optimal result for a shipping dominated environment. Since shipping noise is dominant at lower frequencies 1000 Hz, we expect that high frequency will yield the most complete, uniformly converging, two-sided wave fronts predicted by theory. Further experiments in this higher frequency regime are expected to provide insights into the convergence time of this process. The results presented here are a first step toward passive tomographic imaging. ACKNOWLEDGMENTS This research was supported by the Office of Naval Research. The authors would like to thank Erin Oleson for her help in acquiring sonobuoy data during a Scripps experiment conducted by John Hildebrand s group and W. S. Hodgkiss, H. C. Song, and K. Sabra for valuable discussions. 1 M. J. Buckingham, B. V. Berkhouse, and S. A. L. Glegg, Passive imaging of targets with ambient noise, Nature London 365, G. M. Wenz, Acoustic ambient noise in the ocean: Spectra and sources, J. Acoust. Soc. Am. 34, R. K. Andrew, B. M. Howe, J. M. Mercer, and M. Dzieciuch, Ocean ambient sound: Comparing the 1960s with the 1990s for a receiver off the California coast, Acoustic Res. Letters Online, 3, In this paper, Wenz s results have been compared against more recent data. 4 R. J. Urick, Ambient Noise in the Sea Peninsula, Los Altos, D. Ross, Mechanics of Underwater Noise Peninsula, Los Altos, Estimates of shipping densities given extrapolate to a distribution with more than 1 ship per square degree which suggests and has been confirmed for many years in the field of Underwater Acoustics that except for nearby specific ship tracks, distant shipping can be considered to be smeared out over the large surface of the ocean, albeit with a directional dependence. 6 W. A. Kuperman and F. 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Jensen, A full wave solution for propagation in multi-layered visco-elastic media with application to Gaussian beam reflection at fluid-solid interfaces, J. Acoust. Soc. Am. 77, See also Ref. 16, pp P. Roux and M. Fink, Green s function estimation using secondary sources in a shallow water environment, J. Acoust. Soc. Am. 113, This theoretical paper actually averages over depth for an inserted source and in a sense yields results closer to the Weaver equipartition results. 21 The North Pacific Acoustic Laboratory NPAL experiments were designed to study coherence of acoustic signal propagating long distances in the ocean. The acoustic source was 3000 km from the arrays. The NPAL group provided us with noise data from their receiver array during times when their source was not transmitting. Their array technology is the same used in the Acoustic Thermometry of the Ocean Climate experiments ATOC Consortium, Ocean climate change: comparison of acoustic tomography, satellite altimetry and modeling, Science 281, The data occasionally showed distinct correlation building up over 20 s intervals. A typical ship might have a source level of 165 db and at 100 Hz, a transmission loss of order 80 db see Ref. 5, p. 12. The ambient noise is about 90 db so that the SNR 5 db. With a time-bandwidth product 50 (Hz)20 (s) 30 db, we definitely should see occasional distinct correlation patterns compressed by the ship bearing projection onto the line between the two receivers. 23 H. Schmidt and W. A. Kuperman, Estimation of surface noise source level from low-frequency seismo-acoustic ambient noise measurements, J. Acoust. Soc. Am. 84, J. S. Perkins, W. A. Kuperman, F. Ingenito, L. T. Fialkowski, and J. Glattetre, Modeling ambient noise in three-dimensional ocean environments, J. Acoust. 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